Answer:
x = (e^3 +3)/(e^3 -1) ≈ 1.20958
Step-by-step explanation:
Take the antilog and solve in the usual way.
ln(x+3) -ln(x -1) = 3
ln((x +3)/(x -1)) = 3 . . . . rearrange to a single log
(x +3)/(x -1) = e^3 . . . . take the antilog
x +3 = e^3·(x -1)
3 +e^3 = x(e^3 -1)
x = (e^3 +3)/(e^3 -1) ≈ 1.20958
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Check
This answer checks OK in the original equation:
ln(4.20958) -ln(0.20958) = 3
